Carola Eschenbach

An Axiomatic Approach to the Spatial Relations Underlying Left-Right and in Front of-Behind

This paper presents an axiomatic characterization of spatial orderings in the plane and of concepts underlying intrinsic and deictic uses of spatial terms such as in front of, behind, left and right. This characterization differs in several aspects from existing theories that either employ systems of coordinate axes or systems of regions to specify the meaning of such expressions. We argue that the relations given by in front of and behind can be modeled on the basis of linear orders and on the basis of axes, whereas the relations given by left and right can be modeled as planar and on the basis of regions. The explicit characterization of the means necessary to specify the intrinsic and deictic uses thereby sheds light on the structures contributed by different frames of reference and therefore contributes to understanding the deictic/intrinsic-distinction.

Remarks on plural anaphora

The interpretation of plural anaphora often requires the construction of complex reference objects (RefOs) out of RefOs which were formerly introduced not by plural terms but by a number of singular terms only. Often, several complex RefOs can be constructed, but only one of them is the preferred referent for the plural anaphor in question. As a means of explanation for preferred and non-preferred interpretations of plural anaphora, the concept of a Common Association Basis (CAB) for the potential atomic parts of a complex object is introduced in the following. CABs pose conceptual constraints on the formation of complex RefOs in general. We argue that in cases where a suitable CAB for the atomic RefOs introduced in the text exists, the corresponding complex RefO is constructed as early as in the course of processing the antecedent sentence and put into the focus domain of the discourse model. Thus, the search for a referent for a plural anaphor is constrained to a limited domain of RefOs according to the general principles of focus theory in NLP. Further principles of interpretation are suggested which guide the resolution of plural anaphora in cases where more than one suitable complex RefO is in focus.

Abstract Structures in Spatial Cognition

The importance of studying spatial cognition in cognitive science is enforced by the fact that the applicability of spatial concepts and spatial expressions is not limited to the spatial domain. We claim that common structures underlying both concrete, physical space and other domains are the basis for using spatial expressions, e.g., prepositions like between, with respect to space as well as time or other domains. This claim opposes the thesis that the common use is based upon an analogy between concrete space and other domains. The development of geometry from Euclids Elements to more differentiated systems of diverse geometries and topologies can be perceived of as an example of the transfer from modeling concrete space towards describing abstract spatial structures.

Lexical Specifications of Paths

Natural language descriptions of motion frequently combine verbs of motion and directional prepositions. This article presents an analysis of German expressions from these two classes and their interaction. The focus is on the spatial structures (called path) that link them. Paths and the relations accessing them are formally specified in a geometric framework and with reference to the situation structure. The analysis distinguishes verbs of motion from other kinds of verbs that combine with directional adverbs. In addition, it provides a basis for explaining certain restrictions in combining verbs of motion with directional prepositional phrases and for comparing different approaches to the same kind of expressions.

A Predication Calculus for Qualitative Spatial Representations

Spatial information is information bound to spatial entities such as regions. It is based on the spatial structure alone (the valley includes the field) or connects thematic predicates with spatial entities (Joan Smith owns the field). Formal models of spatial information are concerned with the question of how the structure of space is related to inferences about spatial information. Therefore, in addition to formal models of the structure of space, formal models of the interrelation between thematic information and spatial entities have to be developed. This article addresses the relation between regions and thematic information. It presents a calculus of spatial predicators that is coping with qualitative distinctions, i.e., the mereological and topological structure of space. The spatial structure is given by the Closed Region Calculus, which provides the same terminology as RCC, but has finite models. The spatial predication calculus specifies the interaction of the spatial structure with the thematic information and provides a flexible tool for the representation of and inferences on spatial information.

Geometric structures of frames of reference and natural language semantics

This article aims at formal specifications of reference systems in spatial cognition. It concentrates on two roles of reference systems connected to spatial language: reference systems resolving ambiguities and reference systems forming a basis for the classification of linguistic terms. Although coordinate systems are often seen as candidates for the geometric structure of reference systems, it is shown here that they do not appear in the explanations that go into the details. An analysis of the German terms vor, hinter, rechts and links (in front of, in back of, right, left) presents an alternative model for the geometric structure of spatial reference systems.

A geometric agent following route instructions

We present the model of a Geometric Agent that can navigate on routes in a virtual planar environment according to natural-language instructions presented in advance. The Geometric Agent provides a new method to study the interaction between the spatial information given in route instructions and the spatial information gained from perception. Perception and action of the Geometric Agent are simulated. Therefore, the influence of differences in both linguistic and perceptual skills can be subject to further studies employing the Geometric Agent. The goal of this investigation is to build a formal framework that can demonstrate the performance of specific theories of the interpretation of natural-language in the presence of sensing. In this article, we describe the main sub-tasks of instructed navigation and the internal representations the Geometric Agent builds up in order to carry them out.

Towards a formalization of social spaces for socially aware robots

This article presents a taxonomy of social spaces distinguishing five basic types: personal space, activity space, affordance space, territory, and penetrated space. The respective space-constituting situations and the mereotopological structure for each social space type are specified. We show how permissions for actions of agents in social spaces can be modeled using the situations calculus. Specifications of social spaces and permissions build the fundament for socially aware action planning.

Viewing composition tables as axiomatic systems

Axiomatic systems and composition tables are often seen asalternative ways of specifying the semantic interrelations ofrelations for qualitative reasoning. Axiomatic characterizationsusually specify ontological assumptions concerning the domain ofthe relations and introduce a taxonomic system of relations that,on the one hand, serves to specify the relations and, on the otherhand, supports the communication of the intended meaning.In thisarticle, composition tables are seen as a specific form ofaxiomatic theories that can also be combined with a taxonomicsystem of relations. On this basis, the content of compositiontables can be reformulated in a simplified way. This simplificationsupports the construction of such tables parallel to thedevelopment of the axiomatic specification or on the basis of agiven axiomatic characterization.

Linking spatial haptic perception to linguistic representations: assisting utterances for tactile-map explorations

Assisting utterances are helpful for blind and visually impaired map users exploring tactile maps. Virtual tactile maps explorable by haptic human-computer interfaces form the basis for multimodal presentations including automatically generated assisting utterances. This paper presents first empirical results regarding the type of utterances suitable for assisting the acquisition of survey knowledge on the basis of virtual tactile maps. The structure of the internal knowledge base, which has to support a connection between dynamic exploration movements and natural language, is presented. An example illustrates the approach and shows its practicability.